The fur’s flying in the Hamptons, with no fewer than three animal charities throwing competing benefits tonight hosted by socialites, reality stars and models. Last Chance Animal Rescue will have its annual Martinis 4 Mutts event at Season of Southampton, hosted by “Real Housewife” Sonja Morgan and Social Life magazine, while at the Surf Lodge, Amanda Hearst and pregnant Georgina Bloomberg support the Humane Society’s anti-puppy-mill committee Friends of Finn. And Christie Brinkley’s being honored at the Pet Philanthropy Circle’s Pet Hero Awards at the Water Mill estate of Bob and Jewel Morris. “They are all going for the same audience,” a Hamptons fixture said of the competing events.